• January 22, 2021, 06:42:35 PM
  • Welcome, Guest
Please login or register.

Login with username, password and session length
Advanced search  


Time Zone converter can be found here which is useful for Challenges.

Pages: [1]   Go Down

Author Topic: Project Overview  (Read 2690 times)


  • Board Lord
  • *****
  • Aussie Karma: +2483/-0
  • Offline Offline
  • Posts: 10140
    • Parliament Hill Webcam
Project Overview
« on: March 17, 2015, 02:13:10 PM »

Currently only the Windows application works

Project Summary

The sequence of colors BRRBBRRB (where B is blue and R is red) does not have an evenly spaced subsequence of length 3 that are the same color. However, if you add a B to the end, you get BRRBBRRBB, which has the same color B in positions 1,5, and 9 which are evenly spaced 4 apart. If you add an R to the end, you get BRRBBRRBR, which has R at position 3, 6, and 9. In fact, with only two colors, there is no sequence of length 9 of Bs and Rs that does not have a subsequence of 3 evenly spaced of the same color. Van der Waerden's Theorem states that for any number of colors r and length k, a long enough sequence always has an evenly spaced subsequence of the same color. The smallest length guaranteed to have an evenly spaced subsequence is called the Van Der Waerden Number and is written W(k,r). For example, W(3,2)=9. This project is to find better lower bounds for Van Der Waerden Numbers by finding sequences like BRRBBRRB. See a table of the results so far below.

Here is how the program works. Take a prime number n(shown in parentheses on the table) and a primitive root of that number. For example, let n equal 11. See that W(4,2)-length 4, 2 colors has 11 in parentheses. Let's use the primitive root 2. 2 is a primitive root of 11 because its powers up to 2^10 [2,4,8,16,32,64,128,256,512,1024] modulo 11 (the remainder when dividing by 11) are all distinct and equal [2,4,8,5,10,9,7,3,6,1] which we color red, blue, red, blue. Now all we have to do is reorder this is sequence, getting us [1,2,3,4,5,6,7,8,9,10]. It is proven that we can add the color 11, which should be blue (not bold). It is also proven that we can concatenate 3 more copies of this 11-term sequence while avoiding 4 evenly spaced of the same color. It is also proven we can add a 34th term, so we will. We have just found that W(4,2)-subsequence length 4, 2 colors equals 35. Note it does not equal 34 because this table shows the minimum length that guarantees an evenly spaced sequence of the same color, not the maximum length that can be reached without an evenly spaced sequence of the same color.


Microsoft Windows (98 or later) running on an Intel x86-compatible CPU    
Linux running on an AMD x86_64 or Intel EM64T CPU    

Connecting to Project

The projects Home Page and URL to connect is:


Team Page            
Team Members      [ur]]]

Team Members      [ur]][/url]
Team Members      [ur][/url]
« Last Edit: March 21, 2015, 02:50:21 AM by Dingo »

Have a look at the BOINC@AUSTRALIA Facebook Page and join and also the Twitter Page.

Proud Founder and member of BOINC@AUSTRALIA

HERE are my Primes from Primegrid

Have a look at my  Web Cam of Parliament House Ottawa, CANADA
Pages: [1]   Go Up

Page created in 0.101 seconds with 21 queries.